**Tung H. Nguyen**

**Email:** tunghn [at] math.princeton.edu

**Office:** 218 Fine Hall, Washington Road, Princeton, NJ 08544

Hello! I am Tung Nguyen, a fourth-year PhD student in the Program in Applied and Computational Mathematics at Princeton University, working with Paul Seymour. Before Princeton, I earned a Bachelor of Science (with Honors) in Mathematical Sciences from KAIST, where my thesis advisor was Sang-il Oum.

My Vietnamese name is *Nguyễn Huy Tùng*.

I am interested in discrete mathematics, mostly structural and extremal problems in graph theory.

I have maintained the lists of problems submitted to two Barbados graph theory workshops: 2022a and 2024.

**Papers**

**Preprints**

- A counterexample to the coarse Menger conjecture (with Alex Scott and Paul Seymour), manuscript.
- Induced subgraph density. VII. The five-vertex path (with Alex Scott and Paul Seymour), preprint.
- Induced subgraph density. VI. Bounded VC-dimension (with Alex Scott and Paul Seymour), preprint.
- Induced subgraph density. V. All paths approach Erdős–Hajnal (with Alex Scott and Paul Seymour), preprint.
- Induced subgraph density. IV. New graphs with the Erdős–Hajnal property (with Alex Scott and Paul Seymour), preprint. [A talk by me]
- Induced subgraph density. III. Cycles and subdivisions (with Alex Scott and Paul Seymour), preprint.
- Induced subgraph density. II. Sparse and dense sets in cographs (with Jacob Fox, Alex Scott, and Paul Seymour), preprint.
- Induced subgraph density. I. A $\text{loglog}$ step towards Erdős–Hajnal (with Matija Bucić, Alex Scott, and Paul Seymour), preprint. [A talk by Paul]
- Some results and problems on tournament structure (with Alex Scott and Paul Seymour), preprint.
- A note on the Gyárfás–Sumner conjecture (with Alex Scott and Paul Seymour), preprint.
- Linear-sized minors with given edge density, preprint.
- Polynomial bounds for chromatic number. VIII. Excluding a path and a complete multipartite graph
(with Alex Scott and Paul Seymour),
*J. Graph Theory*, accepted. - Highly connected subgraphs with large chromatic number,
*SIAM J. Discrete Math.*, accepted.

**Published**

- Clique covers of $H$-free graphs
(with Alex Scott, Paul Seymour, and Stephan Thomassé),
*European J. Combin.***118**(2024), Paper No. 103909, 10 pp. - On a problem of El-Zahar and Erdős
(with Alex Scott and Paul Seymour),
*J. Combin. Theory Ser. B***165**(2024), 211–222. [A talk by Alex] - Induced paths in graphs without anticomplete cycles
(with Alex Scott and Paul Seymour),
*J. Combin. Theory Ser. B***164**(2024), 321–339. - A further extension of Rödl's theorem,
*Electron. J. Combin.***30**(2023), no. 3, Paper No. 3.22, 16pp. - Growing balanced covering sets,
*Discrete Math.***344**(2021), no. 11, Paper No. 112554, 6pp. - The average cut-rank of graphs
(with Sang-il Oum),
*European J. Combin.***90**(2020), Paper No. 103183, 22 pp.